An optimization approach for large scale simulations of discrete fracture network flows

In recent papers [1], [2] the authors introduced a new method for simulating subsurface flow in a system of fractures based on a PDE-constrained optimization reformulation, removing all difficulties related to mesh generation and providing an easily parallel approach to the problem. In this paper we further improve the method removing the constraint of having on each fracture a non-empty portion of the boundary with Dirichlet boundary conditions. This way, Dirichlet boundary conditions are prescribed only on a possibly small portion of DFN boundary. The proposed generalization of the method in [1], [2] relies on a modified definition of control variables ensuring the non-singularity of the operator on each fracture. A conjugate gradient method is also introduced in order to speed up the minimization process.